Linux only: The Ubuntu Unleashed blog has a great tutorial on remote controlling your Linux system—even through a Java-enabled browser. Here's the whole deal:

Install packages. Code: sudo apt-get install x11vnc vnc-java

Set up a password for clients. Code: x11vnc -storepasswd

Open up ports 5800 and 5900 on your firewall

Run the terminal command: x11vnc -forever -usepw -httpdir /usr/share/vnc-java/ -httpport 5800 and add it for auto-starting in future sessions

That third step isn't quite so simple, but luckily we've covered that ground before. The same warnings and disclaimers about running a VNC server in that link above apply here. While the guide and code are written from an Ubuntu users' perspective, the packages and commands, possibly with a little tweaking, should be available in most distributions. Windows and Mac users can get help setting up their own VNC connections through this guide.